Lesson 153
AVL Trees
Balance Factor · Rotations · O(log n)
1:00How AVL trees use balance factors and rotations to keep a BST at O(log n) height — covering all four imbalance cases, the Fibonacci-tree height proof, and AVL vs red-black tradeoffs.
By the end, you can
- Explain why sorted insertions degrade a BST to O(n) and why that motivates self-balancing.
- Define balance factor, compute it by hand for any node, and state the AVL invariant.
- Identify which of the four imbalance cases (LL, RR, LR, RL) applies from the balance factors of a node and its child.
- Describe the rotation(s) needed for each case and trace the resulting node positions.
- State the rebalancing cost difference between AVL insert (at most one rotation) and AVL delete (up to O(log n) rotations).
- Explain the Fibonacci-tree argument for why AVL height is O(log n).
- Compare AVL and red-black trees and choose the right one for a given workload.
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